I looked at the photos on Amazon and it looks like it locks on the modern zerk fittings and would not work on the original Model a Ford grease fittings.
I've never seen one of these and checked it out on Amazon. It has a lot of good reviews. One bad feature is that it won't fit in a tight spot, but I think it would work well on modern Model A fittings. It's worth a try as I hope it will eliminate wiping off excess grease.